Stacking dependence of carrier interactions in multilayer graphene systems

We identify qualitative trends in the stacking sequence dependence of carrier-carrier interaction phenomena in multilayer graphene. Our theory is based on an approach which explicitly exhibits the important role in interaction phenomena of the momentum-direction-dependent intersite phases determined by the stacking sequence. Using this method, we calculate and compare the self-energies, density-density response functions, collective modes, and ground-state energies of several different few-layer graphene systems. The influence of electron-electron interactions on important electronic properties can be understood in terms of competition between intraband exchange, interband exchange, and correlation contributions that vary systematically with the stacking arrangement.

Figure 1

Stacking diagrams and phase factor chirality parameters $\left\{P_i\right\}$ for (a) ABC and (b) ABA graphene. (c) Phase factors for all stacking arrangements from monolayers to tetralayers. We have chosen to set the phase factor of the sublattice 1A to zero. These results are for valley $K$. For valley $K^{\prime }$, the chirality parameters change sign.

Figure 2

(a) Exchange self-energies and (b) conduction band pseudospin direction ($s=+1$) for C2DESs with $J=1,2,3,4$. Exchange self-energies of (c) the lowest conduction band ($s=+1$) of ABC trilayer graphene for $n={10}^{11},{10}^{13}{\mathrm{cm}}^{-2}$, and (d) the lowest ($s=+1$) and second lowest ($s=+2$) conduction bands of ABA trilayer graphene for $n={10}^{12}{\mathrm{cm}}^{-2}$. (The bands of the ABA multilayer structures are shown in the inset.) Here ${\mathrm{\Sigma }}_0=\frac{2e^2{k}_{\mathrm{F}}}{{\epsilon }_0\pi }$ and we use the effective fine structure constant $\alpha =\frac{e^2}{{\epsilon }_0\hslash v}=1$ and momentum cutoff $q_c=1/a$.

Figure 3

Loss function $\mathrm{Im}[-\varepsilon {(q,\omega )}^{-1}]$ of (a) ABC, (b) ABA, (c) ABCA, and (d) ABAB stacked multilayer graphene for $n={10}^{12}{\mathrm{cm}}^{-2}$ and $\alpha =1$ with $\eta =5\times {10}^{-5}{\varepsilon }_{\mathrm{F}}$. The thick black lines indicate boundaries of the electron-hole continua and the insets in each panel show the energy band structure. In the ABA structure and in other multilayer structures with mirror symmetry, some interband transitions do not contribute to plasmon Landau damping, as indicated by the dotted lines in (b).

Figure 4

Comparison between the ground-state exchange energies (left panel) and correlation energies (right panel) of several different multilayer graphene (thick lines) structures and C2DES systems (dotted lines) as a function of carrier density for $\alpha =0.05$.